Mohamed Rhaima

📢 Call for Papers — ICoIAM 2025 📢 The International Conference of Industrial and Applied Mathematics (ICoIAM 2025) will be held in Hammamet, Tunisia, at the TUI MAGIC LIFE Africana hotel, from December 19–21, 2025. 🔹 Topics of Interest include: Mathematical Modeling & Simulation Optimization & Operations Research Differential Equations & Dynam...

This paper investigates Entangled Hidden Markov Models (EHMMs), with a particular focus on how entanglement influences quantum dynamics. We present a structure theorem for inhomogeneous EHMMs, which provides a foundational understanding of their behavior in complex systems. Furthermore, we compute the Ohya degree of entanglement for models with det...

This work focuses on implementing [Formula: see text] Observer-Based Control (OBC) for a class of Nonlinear Conformable fractional-order Delayed Systems (NCDSs) represented by the Takagi–Sugeno fuzzy model (TSFM). The aim is to develop conditions, utilizing the Lyapunov approach, that guarantee the existence of both a controller and an observer. Th...

In this work, we derive combinatorial properties of the degenerate falling operators, present their connections with a generalization of the Appell polynomials \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\...

While the \(H_\infty \) observer-based control has found widespread application in the literature for integer-order systems, researchers have shown less interest in addressing the same issue within the fractional-order framework. In this context, this study delves into the application of \(H_\infty \) observer-based control for the Hadamard fractio...

This research focuses on exploring the exponential \(H_\infty \) stability of general conformable nonlinear system. In order to address the nonlinearity inherent in the system, a polynomial fuzzy (PF) method is employed. Modeling a general conformable nonlinear system within the polynomial framework reduces the number of fuzzy rules compared to the...

This paper explores the existence, uniqueness, and averaging principles of neutral fractional stochastic Itô–Doob differential equations (NFSIDDEs). By utilizing the Picard iteration technique (PIT), we establish the existence and uniqueness of solutions. Additionally, we demonstrate the averaging principle for NFSIDDEs through the utilization of k...

The paper deals with ‐tempered fractional derivatives, along with their stability properties. Firstly, we obtain the derivative inequalities, which are essential in applying the theorems derived in this work. Then, by using Lyapunov function, we obtain the stability results of such systems. Furthermore, an observer design is given as an application...

This study delves into the formulation of innovative integral inequalities, specifically designed to accommodate weakly singular singularities, thus significantly broadening the scope of previously established ones. The methodology employed centers around the application of weighted fractional differential equations, leading to the derivation of a...

The main purpose of this paper is to derive a general new structure of generalized noise analysis by using the interacting Fock space techniques. First, we start with a detailed construction of the interacting Fock space which serves to obtain the quantum decomposition of such random variables as sums of creation, annihilation and preservation oper...

This paper examines the properties of finite-time stability (FTS) in the sense of Hadamard fractional-order systems. The investigation utilizes the Hadamard fractional derivative to formulate and analyze these systems, establishing FTS criteria based on the Lyapunov theory. Additionally, this paper presents a comprehensive exploration of methodolog...

Due to the significance of its integer-order counterpart in numerous mathematical and engineering fields, this paper investigates the fractional-order Laguerre polynomials. The primary objective is to construct and highlight specific properties of a novel polynomials sequence termed Fractional Laguerre Appell polynomials. These polynomials are asso...

This paper addresses the existence and exponential stability problem of highly nonlinear hybrid neutral pantograph stochastic equations with multiple delays (HNPSDEswMD). By Lyapunov functional method and without laying down a linear growth condition, the above problem of the exact solution is shown. We end up with two numerical examples that corro...

In this work, we employ a biorthogonal approach to construct the infinite-dimensional Fractional Pascal measure \(\mu ^{(\alpha )}_{_{\sigma }}, 0 < \alpha \le 1\), defined on the tempered distributions space \(\mathcal {E}'\) over \(\mathbb {R} \times \mathbb {R}^{*}_{+}\). The Hilbert space \(L^{2}(\mu ^{(\alpha )}_{_{\sigma }})\) is characterize...

The International Conference on Fractional Calculus and Applications is a prestigious event that serves as a platform for researchers, scientists, and practitioners to exchange ideas and explore the latest advancements in the field of fractional calculus. The conference aims to foster collaboration and innovation in this rapidly evolving field. Our...

For fractional-order systems, observer design is remarkable for the estimation of unavailable states from measurable outputs. In addition, the nonlinear dynamics and the presence of parameters that can vary over different operating conditions or time, such as load or temperature, increase the complexity of the observer design. In view of the aforem...

This study addresses the challenge of synchronizing master and slave systems in complex dynamic networks using Takagi-Sugeno (T-S) fuzzy Markovian jump models, with the presence of coupling delays. To enhance synchronization robustness, fault-tolerant control mechanisms are implemented. State feedback controller is converted to fault-tolerant contr...

This article investigates the finite-time (FT) boundedness problem for the time delay (TD) Takagi–Sugeno fuzzy model (TSFM) with conformable derivative (CD) and in the presence of certain actuator faults. Through the reconstruction of an appropriate Lyapunov–Krasovskii functional, some sufficient conditions expressed by the linear matrix inequaliti...

In this paper, we present the existence of a mild solution for a class of a neutral stochastic integro-differential system over a Hilbert space. Such systems are influenced by both multiplicative and fractional noise, alongside non-instantaneous impulses, with a Hurst index H in the interval (12,1). Additionally, the systems under consideration fea...

This paper focuses on solving the challenge of observer-based exponential control (O-BC) regarding conformable fuzzy polynomial models with time delay. In this work, polynomial matrices with unmeasurable states are considered to enhance the practicality of the model in the design problem. The proposed approach guarantees the existence of the polyno...

This paper investigates the qualitative properties of the solutions for neutral implicit stochastic Hilfer fractional differential equations involving Lévy noise with retarded and advanced arguments. The existence property of the solution of the aforementioned equation is demonstrated by the Mónch condition, and the uniqueness is demonstrated by th...

This paper presents an extensive investigation into the state feedback stabilization, observer design, and observer-based controller design for a specific category of nonlinear Hadamard fractional-order systems. The research extends the conventional integer-order derivative to the Hadamard fractional-order derivative, offering a more universally ap...

We investigated a novel stochastic fractional partial differential equation (FPDE) characterized by a mixed operator that integrated the standard Laplacian, the fractional Laplacian, and the gradient operator. The equation was driven by a random noise, which admitted a covariance measure structure with respect to the time variable and behaved as a...

This paper extended the framework of quantum Markovianity by introducing backward and inverse backward quantum Markov chains (QMCs). We established the existence of these models under general conditions, demonstrating their applicability to a wide range of quantum systems. Our findings revealed distinct structural properties within these models, pr...

This paper introduces a sum-of-squares (S-O-S) approach to Stability Analysis and Stabilization (SAS) of nonlinear dynamical systems described by General Conformable Polynomial Fuzzy (GCPF) models with a time delay. First, we present GCPF models, which are more general compared to the widely recognized Takagi–Sugeno Fuzzy (T-SF) models. Then, we es...

This paper offers a comprehensive analysis of solution representations for ϖ-fractional partial differential equations, specifically focusing on the linear case of the Darboux problem. We exhibit a representation of the solutions for the Darboux problem of ϖ-fractional partial differential equations in the linear case in the space of continuous fun...

In this study, we explore the existence and uniqueness of solutions for a boundary value problem defined by coupled sequential fractional differential inclusions. This investigation is augmented by the introduction of a novel set of generalized Riemann–Liouville boundary conditions. Utilizing Carathéodory functions and Lipschitz mappings, we establ...

In this study, we focus on the stability analysis of the RLC model by employing differential equations with Hadamard fractional derivatives. We prove the existence and uniqueness of solutions using Banach’s contraction principle and Schaefer’s fixed point theorem. To facilitate our key conclusions, we convert the problem into an equivalent integro-...

Entangled hidden Markov models (EHMMs) extend classical hidden Markov models into the quantum domain, while elephant random walks (ERWs) are globally inhomogeneous Markov processes with memory-dependent steps. In this paper, we propose a novel approach that combines EHMMs with ERWs. Our focus is on exploring the correlations within an EHMM associat...

In this article, we will examine the finite time stability (FTS) of ‐Caputo neural network fractional systems (NNFS) with an order of . Utilizing technical inequalities such as Gronwall and Hölder inequalities, we present some FTS results. Two numerical examples are provided to illustrate the theoretical findings.

The goal of this paper is to present new results on the general structure of fractional Lévy–Meixner noise functionals. More precisely, we construct and emphasize certain properties of a new Appell polynomials associated with the infinite-dimensional Fractional Lévy–Meixner noise measure. Furthermore, we explore the relationship between new polynom...

We construct an infinite dimensional analysis with respect to non-Gaussian measures of fractional Gamma type which we call fractional Gamma noise measures. It turns out that the well-known Wick ordered polynomials in Gaussian analysis cannot be generalized to this non-Gaussian case. Instead of using generalized Appell polynomials we prove that a sy...

This paper investigates the development of a novel analytic approach for computing Unity Magnitude (UM) shapers that deviates from established numerical methodologies. The experimental validation on a test bench confirms the practicality and benefits of the suggested UM shaper technique. The study extends the use of UM shapers to improve the contro...

The focus of this study is on modeling and management of a Wind Energy Conversion System (WECS) based on a Hybrid Excitation Synchronous Generator (HESG). Using a wind simulator, two controllers, CRONE and H ∞ , are evaluated for Maximum Power Point Tracking (MPPT) and optimal rotation speed. The results show the CRONE controller's higher tracking...

This study investigates the existence and Ulam-Hyers stability (UHS) results in the context of mixed Hadamard and Riemann-Liouville Fractional Stochastic Differential Equations (HRFSDEs). The primary focus is on establishing the existence and uniqueness of solutions through the application of the Banach Fixed point Theorem (BFT) coupled with standa...

Dual Excitation Generators (DESGs) are a new, promising form of high-efficiency generator. However, maximizing their performance and control tactics is still a difficult task. This study will address this issue by studying a 1.5 MW DESG and proposing an analytical sizing approach to establish important electrical characteristics for optimal control...

This paper explores a fractional integro-differential equation with boundary conditions that incorporate the Hilfer-Hadamard fractional derivative. We model the RLC circuit using fractional calculus and define weighted spaces of continuous functions. The existence and uniqueness of solutions are established, along with their Ulam-Hyers and Ulam-Hye...

In this study, we delve into the examination of Finite Time Stability (FTS) within a specific class of Fractional-Order Systems (FOS) with time delays. By applying a fixed-point theorem, we establish novel sufficient conditions to ensure FTS for time-delayed FOS within 1<σ<2. Moreover, we investigate the existence and uniqueness of global solutions...

The aim of this paper is to define the generalized discrete proportional derivative (GDPD) and illustrate the application of the Leibniz theorem, the binomial expansion, and Montmort’s formulas in the context of the generalized discrete proportional case. Furthermore, we introduce the generalized discrete proportional Laplace transform and determin...

This research addresses the problem of globally stabilizing a distinct category of fractional-order power systems (F-OP) by employing an observer-based methodology. To address the inherent nonlinearity in these systems, we leverage a Takagi–Sugeno (TS) fuzzy model. The practical stability of the proposed system is systematically established through...

In this paper, we investigate the existence and uniqueness properties pertaining to a class of fractional Hadamard Itô–Doob stochastic integral equations (FHIDSIE). Our study centers around the utilization of the Picard iteration technique (PIT), which not only establishes these fundamental properties but also unveils the remarkable averaging princ...

In this study, we explore the realm of practical stability within stochastic functional differential equations with infinite delay (SFDEID). Specifically, we investigate the notions of pth moment and almost sure stability and develop a fresh set of criteria to effectively assess and quantify these properties. To showcase the practical significance...

An investigation of the input-to-state practical stability (ISpS) and the integral input-to-state practical stability (iISpS) of nonlinear systems with time delays (NSWTDs) is presented in this paper. The ISpS and iISpS of the systems are obtained by using a continuously differentiable Lyapunov–Krasovskii functional (LKF) within-definite derivative...

The study of the existence and uniqueness of solutions to 2D systems utilizing the generalized proportional fractional derivative operator is the focus of this work. We also derive a finite difference scheme in order to numerically approximate such an operator, and we prove that the method we propose is convergent. Several tests are performed at th...

This study focuses on implementing a wind turbine emulator based on a permanent magnet synchronous machine with excitation auxiliary windings and thoroughly investigates the space harmonics created by this innovative topology in MATLAB/Simulink. A Hybrid Generator (HG) is a robust generator that does not have slip rings or brushes in its structure....

This paper investigates the finite-time stability (FTS) of a linear conformable stochastic differential equation with finite delay (LCSDEwFD). We use the Banach fixed point theorem (BFPT) to prove the existence and uniqueness of the solution and analyze the FTS of the system using the Gronwall inequalities. To demonstrate the practical value of our...

In networks, the Markov clustering (MCL) algorithm is one of the most efficient approaches in detecting clustered structures. The MCL algorithm takes as input a stochastic matrix, which depends on the adjacency matrix of the graph network under consideration. Quantum clustering algorithms are proven to be superefficient over the classical ones. Mot...

In this study, linear Fredholm fractional integro-differential equations (FIDEs) are numerically solved, where the fractional derivative is considered in the Caputo sense. In this work, the least squares method (LSM) using a compact combination of shifted Chebyshev polynomials (SCP) of the first Kind is applied to solving a class of FIDEs. Our aim...

Fractional systems have been widely utilized in various fields, such as mathematics, physics and finance, providing a versatile framework for precise measurements and calculations involving partial quantities. This paper aims to develop a novel polynomial controller for a power system (PS) with fractional-order (FO) dynamics. It begins by studying...

The issue of extended dissipative analysis for neural networks (NNs) with additive time-varying delays (ATVDs) is examined in this research. Some less conservative sufficient conditions are obtained to ensure the NNs are asymptotically stable and extended dissipative by building the agumented Lyapunov-Krasovskii functional, which is achieved by uti...

In this paper, we investigate the Darboux problem of conformable partial differential equations (DPCDEs) using fixed point theory. We focus on the existence and Ulam–Hyers–Rassias stability (UHRS) of the solutions to the problem, which requires finding solutions to nonlinear partial differential equations that satisfy certain boundary conditions. U...

In this study, the Lyapunov technique is used to analyze the observer-based control problem for polynomial fuzzy fractional order (PFFO) models. The case of polynomial matrices with unmeasurable states is considered to increase the applicability of the PFFO models in the design problem. In this regard, we offer two design procedures. First, the des...

In this paper, using a fixed point method, we proved the existence and uniqueness of solutions for a backward differential equation with time advance via ζ−Caputo fractional derivative. Furthermore, the Ulam–Hyers–Rassias and the Ulam–Hyers stabilities of the backward differential equation with time advance via ζ−Caputo fractional derivative are in...

In this study, an unknown input observer is proposed for a class of nonlinear GPFOSs. For this class of systems, both full-order and reduced-order observers have been established. The investigated system satisfies the one-sided Lipschitz nonlinear condition, which is an improvement of the classic Lipschitz condition. Sufficient conditions have been...

The state feedback controller design for a class of Generalized Proportional Fractional Order (GPFO) Nonlinear Systems is presented in this paper. The design is based on the combination of the One-Sided Lipschitz (OSL) system class with GPFO modeling. The main contribution of this study is that, to the best of the authors’ knowledge, this work pres...

In this article, we study the Finite-Time Stability (FTS) of Linear Stochastic Fractional Differential Equations of Itoˆ-Doob Type with Delay (LSFDEIDTwD) for a derivative order q 2 0; 1 ð Þ. In fact, the (FTS) here consists in studying the stability of the (LSFDEIDTwD) in a finite-time domain 0; T ½. To our knowledge, this work represents the firs...

In this research article, we deal with the global convergence of successive approximations (s.a) as well as the existence of solutions to a fractional $ {(p, q)} $-difference equation. Then, we discuss the existence result of the solutions of Caputo-type $ {(p, q)} $-difference fractional vector-order equations in a Banach space. Also, we prove a t...

This article investigates the practical exponential stability and design problems of conformable time-delay systems. Sufficient conditions that confirm the practical exponential stability and design of the proposed class of systems are given by utilizing an adequate Lyapunov–Krasovskii functional (L-KF). These conditions are expressed in the form o...

This paper addresses the existence of stability results for Ulam–Hyers (UHS) and Ulam–Hyers–Rassias (UHRS) in the setting of Caputo–Hadamard fractional functional stochastic differential equations with delay (FFSDEwD). We first prove existence and uniqueness using Banach fixed point theorem coupled with standard stochastic analysis techniques. Then...

In this paper we are interested in solving numerically quadratic SDEs with non-necessary continuous drift of the from Xt = x + ? t 0 b(s,Xs)ds + ? t 0 f (Xs)?2(Xs)ds + ? t 0 ?(Xs)dWs, where, x is the initial data b and ? are given coefficients that are assumed to be Lipschitz and bounded and f is a measurable bounded and integrable function on the...

This work addresses existence and stabilization problem for a hybrid neutral stochastic delay differential equations with Lévy noise (HNSDDELN). The coefficients of such systems do not satisfy the conventional linear growth conditions, but are subject to high nonlinearity. We first prove the existence and uniqueness of the solution. We then design...

Quantum Markov chains (QMCs) on graphs and trees were investigated in connection with many important models arising from quantum statistical mechanics and quantum information. These quantum states generate many important properties such as quantum phase transition and clustering properties. In the present paper, we propose a construction of QMCs as...

The current article is used to investigate the Hyers-Ulam stability (HUS) of Hadamard stochastic fractional differential equations (HSFDE) by using a version of some fixed point theorem (FPT), a technical lemma and some classical stochastic calculus tools. To show the interest of our results, we present two examples. In this manner, we generalize s...

This paper addresses the problem of exponential synchronization in continuous-time complex dynamical networks with both time-delayed and non-delayed interactions. We employ a proportional integral derivative (PID) control strategy and a dynamic event-triggered approach to investigate this synchronization problem. Our approach begins with constructi...

This paper addresses the challenge of ensuring finite-time boundedness in switched time-varying delay systems with actuator saturation. Utilizing Lyapunov–Krasovskii functionals, we establish delay-dependent conditions through linear matrix inequalities, ensuring that switched systems with time-varying delays remain finite-time bounded. The paper a...

In this article, we investigate the existence and uniqueness of solution of controlled hybrid neutral stochastic differential equations with infinite delay (HNSFDEswID). It is known that the time lag generated by the controller in each discrete observation must be different. The controlled HNSFDEswID are affected by the variable delay induced by th...

In this work, we study the almost sure exponential stability (A.S.E.S) and the exponential stability in p‐th moment (E.S.P.M) of conformable stochastic systems depending on a parameter (CSSP) by using the Lyapunov methods and the classical stochastic analysis techniques. In the last section, we apply the main result for an illustrative example.

In this paper, we investigate the partial asymptotic stability (PAS) of neutral pantograph stochastic differential equations with Markovian switching (NPSDEwMSs). The main tools used to show the results are the Lyapunov method and the stochastic calculus techniques. We discuss a numerical example to illustrate our main results.

In this paper, by using the Gronwall inequality, we show two new results on the Ulam-Hyers and the Ulam-Hyers-Rassias stabilities of neutral stochastic functional differential equations. Two examples illustrating our results are exhibited. ARTICLE HISTORY

In this paper, we investigate the partial practical exponential stability of neutral stochastic functional differential equations with Markovian switching. The main tool used to prove the results is the Lyapunov method. We analyze an illustrative example to show the applicability and interest of the main results.

This paper focuses on the finite-time stability of linear stochastic fractional-order systems with time delay for α∈(12,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}...

20 0 0 MSC: 60H10 34K20 34K50 Keywords: Neutral pantograph stochastic differential equations with Markovian switching Lévy noise h-stability pth moment a b s t r a c t In this paper we investigate the h-stability in pth moment of neutral pantograph stochastic differential equations with Markovian switching driven by Lévy noise. The main tool used t...

In this paper we focus on the p-th moment exponential stability of neutral stochastic pantograph differential equations with Markovian switching (NSPDEwMS). By means of the Lyapunov method, we develop some sufficient conditions on the p-th moment exponential stability for NSPDEwMS. We analyze two examples to show the interest of the main results.

In this paper, we investigate the -stability in q-th moment for neutral impulsive stochastic functional differential equations with Markovian switching (NISFDEwMS). Moreover, -stability in q-th moment is studied by using the Lyapunov techniques and a new Razumikhin-type theorem to prove our result. Finally, we check the main result by a numerical e...

The Ulam-Hyers-Rassias stability for stochastic systems has been studied by many researchers using the Gronwall-type inequalities, but there is no research paper on the Ulam-Hyers-Rassias stability of stochastic functional differential equations via fixed point methods. The main goal of this paper is to investigate the Ulam-Hyers Stability (HUS) an...

We introduce a non-commutative extension of the Kronecker product for matrices over C *-algebras. Our main result concerns the complete positivity of a function of the generalized Kronecker product. Relevant examples and counterexamples are investigated.

We express, in full generality, the Jacobi sequences and the orthogonal polynomials of the powers of a real-valued random variable (Formula presented.) with all moments, as functions of the corresponding sequences of the random variable itself.

In the paper Accardi et al.: Identification of the theory of orthogonal polynomials in d–indeterminates with the theory of 3–diagonal symmetric interacting Fock spaces on \(\mathbb {C} ^d\), submitted to: IDA–QP (Infinite Dimensional Anal. Quantum Probab. Related Topics), [1], it has been shown that, with the natural definitions of morphisms and is...

We express the Jacobi sequences of the square of a real valued random variable with all moments, not necessarily symmetric, as functions of the corresponding sequences of the random variable itself. In the symmetric case, the result is known and, we give a short, purely algebraic proof of it. We apply our result to the square of the Gamma distribut...

We prove that, each probability meassure on ℝ, with all moments, is canonically associated with (i) a∗-Lie algebra; (ii) a complexity index labeled by pairs of natural integers. The measures with complexity index (0,K) consist of two disjoint classes: that of all measures with finite support and the semi-circle-arcsine class (the discussion in Sec....